10 questions · Form 5 Mathematics Bab 7: Measures of Dispersion for Grouped Data
For the class interval 20 - 29, what is its lower boundary if the preceding class interval is 10 - 19?
Prefer reading to quizzing? All 10 questions are listed below with the answer and explanation under each one.
1. For the class interval 20 - 29, what is its lower boundary if the preceding class interval is 10 - 19?
Answer: A
Lower boundary = Upper limit of previous class + Lower limit of current class2 = 19 + 202 = 19.5.
2. For N = 200, the first quartile Q₁ occurs at a cumulative frequency of:
Answer: C
Position of Q₁ = (14) × 200 = 50.
3. The interquartile range of a grouped dataset is defined as:
Answer: A
Interquartile range = Third Quartile (Q₃) - First Quartile (Q₁).
4. Given ∑f = 50, ∑fx = 300, and ∑fx² = 2300, calculate the mean x̄.
Answer: A
Mean x̄ = ∑fx / ∑f = 30050 = 6.
5. If total frequency N = 80, at what cumulative frequency do you locate the third quartile (Q₃) on an ogive?
Answer: C
Q₃ corresponds to (34) × N = (34) × 80 = 60.
6. If all frequencies in a grouped dataset are multiplied by a constant factor of 2, what happens to the mean x̄?
Answer: A
Multiplying frequencies uniformly scales total frequency ∑f and ∑fx by 2, leaving mean x̄ = 2∑fx2∑f unchanged.
7. Calculate the class size for the class interval 15 - 19.
Answer: A
Lower boundary = 14.5, Upper boundary = 19.5. Class size = 19.5 - 14.5 = 5.
8. What is the standard deviation σ for a dataset with a variance of 16?
Answer: A
Standard deviation σ = √(Variance) = √16 = 4.
9. Using ∑f = 50, ∑fx = 300, and ∑fx² = 2300, find the variance σ².
Answer: A
Variance σ² = (∑fx² / ∑f) - (x̄)² = (230050) - 6² = 46 - 36 = 10.
10. For a cumulative frequency distribution of N = 120, what cumulative frequency corresponds to the 60th percentile (P₆₀)?
Answer: A
Position of P₆₀ = (60100) × 120 = 72.